A1 Journal article (refereed)
The higher order fractional Calderón problem for linear local operators : Uniqueness (2022)


Covi, G., Mönkkönen, K., Railo, J., & Uhlmann, G. (2022). The higher order fractional Calderón problem for linear local operators : Uniqueness. Advances in Mathematics, 399, Article 108246. https://doi.org/10.1016/j.aim.2022.108246


JYU authors or editors


Publication details

All authors or editorsCovi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther

Journal or seriesAdvances in Mathematics

ISSN0001-8708

eISSN1090-2082

Publication year2022

Volume399

Article number108246

PublisherElsevier

Publication countryNetherlands

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.aim.2022.108246

Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/79921

Publication is parallel publishedhttps://arxiv.org/abs/2008.10227


Abstract

We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the exterior Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations.


Keywordspartial differential equationsinverse problems

Free keywordsFractional Calderón problem; Fractional Schrödinger equation; Sobolev multipliers


Contributing organizations


Ministry reportingYes

Reporting Year2022

JUFO rating3


Last updated on 2024-15-06 at 01:07